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Weak String Erasure: Difference between revisions
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==Properties== | ==Properties== | ||
* If (dishonest) Bob holds a quantum memory of dimension at most <math>d</math>, then his (smooth) min-entropy is lower bounded as follows,</br> | * If (dishonest) Bob holds a quantum memory of dimension at most <math>d</math>, then his (smooth) min-entropy is lower bounded as follows,</br> | ||
<math>H_{\min}^\epsilon(X_1^n | | <math>H_{\min}^\epsilon(X_1^n | K \Theta_1^n M) \geq n \gamma\left(\frac{-\log(d)}{n}\right) -1- \log\frac{2}{\epsilon^2},</math></br> | ||
where <math>K</math> is any classical information Bob can hold, and $M$ represent Bob's quantum state in his memory. This quantum state has dimension at most <math>d</math>. | where <math>K</math> is any classical information Bob can hold, and $M$ represent Bob's quantum state in his memory. This quantum state has dimension at most <math>d</math>. | ||
* Alice is ignorant about the set <math>\mathcal{I}</math>, the set of rounds in which Alice and Bob have chosen the same basis. | * Alice is ignorant about the set <math>\mathcal{I}</math>, the set of rounds in which Alice and Bob have chosen the same basis. | ||
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==Further Information== | ==Further Information== | ||
* The Bounded Storage Model was introduced in [[Weak String Erasure#References| | * The Bounded Storage Model was introduced in [[Weak String Erasure#References|[5], [4] ]] | ||
* The Bounded Storage Model can generalized into the Noisy Storage Models [[Weak String Erasure#References| | * The Bounded Storage Model can generalized into the Noisy Storage Models [[Weak String Erasure#References|[3], [1] ]] | ||
* The security of Weak String Erasure has been analyzed in the presence of noise and losses [[Weak String Erasure#References| | * The security of Weak String Erasure has been analyzed in the presence of noise and losses [[Weak String Erasure#References|[2] ]] | ||
==References== | ==References== | ||
{{Reflist}} | {{Reflist}} | ||